Stability Analysis Of Antibiotic Resistance Infectious Disease Model In Hospital Infection

Increasing antibiotic resistance in common bacterial pathogens, in both hospitals andcommunities, presents a growing threat to human health worldwide, Many scholars havestudied the method to prevent the antibiotic resistance diseases spreading. Limited ther-apeutic options made prevention become increasingly important, thereby bring the imple-mentation of efective infection control strategies to the forefront. Mathematical modelshave also developed to study pharmacodynamics of various antimicrobial therapies. In thispaper, by analyzing the stability of the model and the mechanism of the spread of infectiousdiseases, People can prevent the spread of antibiotic resistance efectively.Firstly, we formulate a model to quantify key elements in nosocomial epidemics aboutantibiotic resistance, we analyze the stability of disease-free equilibrium and endemic equi-librium. We use the Liapunov function proved that the disease-free equilibrium is globallyasymptotically stable when R0≤1. Based on the Krasnoselskii technique, the endemicequilibrium is locally asymptotically stable if RN>1and RR<1. Some numerical simula-tions are given to illustrate the main theoretical results. By means of controlling some usefulparameters we give the changes of R0. From these numerical simulations we can acquirewhat we want.Secondly, we investigate a ODE model and a delay model about the antibiotic resistancein hospitals. By using Lasalle-Liapunov invariant set principle and Routh-Hurwitz crite-rion, we showed that the two models are globally asymptotically stable at the disease-freeequilibrium when R0<1. If R0>1, the endemic equilibriums of the two models are existand they are the same. Then we consider the behavior of the two models around the endemicequilibrium, and show that the endemic equilibrium is locally asymptotically stable of theODE model. However, about the delay model for any τ=0, we obtain the existence con-ditions for Hopf bifurcations at the endemic equilibrium. A series of numerical simulationsare presented to illustrate our mathematical fndings.Finally, we investigate the stability of a delay model about the antibiotic resistance with nonlinear incidence rate in hospitals. A basic reproduction number which determines theoutcome of infectious disease is found, Here we use Lasalle-Liapunov invariant set principleand Routh-Hurwitz criterion obtained that when R0<1the disease-free equilibrium isglobally asymptotically stable; If R0>1, the endemic equilibriums of the model is existand unique, for any τ=0the existence conditions for Hopf bifurcations at the endemicequilibrium are obtained. Then a series of numerical simulations are presented to illustrateour mathematical fndings.